%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL003-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:24:43 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(converse_idempotence_8,axiom,
! [VAR_0] : converse(converse(VAR_0)) = VAR_0,
file('theBenchmark.p',converse_idempotence_8) ).
cnf(c_12,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence_8]) ).
fof(converse_additivity_9,axiom,
! [VAR_0,VAR_1] : converse(join(VAR_0,VAR_1)) = join(converse(VAR_0),converse(VAR_1)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c_13,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity_9]) ).
cnf(c_14,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(copy,[status(thm)],[c_13]) ).
fof(goals_14,axiom,
( join(converse(sk1),converse(sk2)) = converse(sk2)
| join(sk1,sk2) = sk2 ),
file('theBenchmark.p',goals_14) ).
cnf(c_23,plain,
( join(converse(sk1),converse(sk2)) = converse(sk2)
| join(sk1,sk2) = sk2 ),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_65,plain,
( join(converse(sk1),converse(sk2)) = converse(sk2)
| join(sk2,sk1) = sk2 ),
inference(paramod,[status(thm)],[c_1,c_23]) ).
cnf(c_66,plain,
( join(converse(sk2),converse(sk1)) = converse(sk2)
| join(sk2,sk1) = sk2 ),
inference(paramod,[status(thm)],[c_1,c_65]) ).
cnf(c_24,plain,
( converse(join(sk2,sk1)) = converse(sk2)
| join(sk2,sk1) = sk2 ),
inference(paramod,[status(thm)],[c_14,c_66]) ).
fof(goals_17,axiom,
( join(converse(sk1),converse(sk2)) != converse(sk2)
| join(sk1,sk2) != sk2 ),
file('theBenchmark.p',goals_17) ).
cnf(c_25,plain,
( join(converse(sk1),converse(sk2)) != converse(sk2)
| join(sk1,sk2) != sk2 ),
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_67,plain,
( join(converse(sk1),converse(sk2)) != converse(sk2)
| join(sk2,sk1) != sk2 ),
inference(paramod,[status(thm)],[c_1,c_25]) ).
cnf(c_68,plain,
( join(converse(sk2),converse(sk1)) != converse(sk2)
| join(sk2,sk1) != sk2 ),
inference(paramod,[status(thm)],[c_1,c_67]) ).
cnf(c_26,plain,
( converse(join(sk2,sk1)) != converse(sk2)
| join(sk2,sk1) != sk2 ),
inference(paramod,[status(thm)],[c_14,c_68]) ).
cnf(c_69,plain,
( converse(converse(sk2)) = join(sk2,sk1)
| join(sk2,sk1) = sk2 ),
inference(paramod,[status(thm)],[c_24,c_12]) ).
cnf(c_70,plain,
( sk2 = join(sk2,sk1)
| join(sk2,sk1) = sk2 ),
inference(paramod,[status(thm)],[c_12,c_69]) ).
cnf(c_71,plain,
( join(sk2,sk1) = sk2
| join(sk2,sk1) = sk2 ),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_63,plain,
join(sk2,sk1) = sk2,
inference(copy,[status(thm)],[c_71]) ).
cnf(c_72,plain,
( converse(join(sk2,sk1)) != converse(sk2)
| sk2 != sk2 ),
inference(paramod,[status(thm)],[c_63,c_26]) ).
cnf(c_73,plain,
( converse(sk2) != converse(sk2)
| sk2 != sk2 ),
inference(paramod,[status(thm)],[c_63,c_72]) ).
cnf(c_74,plain,
converse(sk2) != converse(sk2),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_64,plain,
$false,
inference(copy,[status(thm)],[c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL003-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 05:23:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2875015 was started by sandbox2 on n007,
% 0.08/0.36 % Sat Sep 26 05:23:24 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 10.
% 0.08/0.38 % Level of proof is 4.
% 0.08/0.38 % Maximum clause weight is 27.000.
% 0.08/0.38 % Given clauses 14.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------